Problem: Solve for $x$ : $2x^2 + 18x + 40 = 0$
Answer: Dividing both sides by $2$ gives: $ x^2 + {9}x + {20} = 0 $ The coefficient on the $x$ term is $9$ and the constant term is $20$ , so we need to find two numbers that add up to $9$ and multiply to $20$ The two numbers $4$ and $5$ satisfy both conditions: $ {4} + {5} = {9} $ $ {4} \times {5} = {20} $ $(x + {4}) (x + {5}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 4) (x + 5) = 0$ $x + 4 = 0$ or $x + 5 = 0$ Thus, $x = -4$ and $x = -5$ are the solutions.